As this site explains, neither word necessarily has any sexual connotations:

The sex-related meanings of words tend to drive out all other
meanings. Most people think of both “perverse” and “perverted” only in
contexts having to do with desire; but “perverse” properly has the
function of signifying “stubborn,” “wrong-headed.”

Nothing erotic is suggested by this sort of thing: “Josh perversely
insisted on carving wooden replacement parts for his 1958 Ford’s
engine.”

It’s better to use “perverted” in relation to abnormal sexual desires;
but this word also has non-sexual functions, as in “The bake-sale was
perverted by Gladys into a fundraiser for her poker habit.”

These sentences place your examples in a context that might make their word choice more clear:

Despite her strait-laced upbringing, Mandy took a perverse interest in photos of boys in Tiger Beat.

Her maternal instincts thwarted, Matilda took a perverted interest in photos of boys in Speedos.